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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 10, Issue 5

Issues

On Courant's nodal domain theorem

Giovanni Alessandrini
Published Online: 2008-03-11 | DOI: https://doi.org/10.1515/form.10.5.521

Abstract

We study the validity of Courant's nodal domain theorem for eigenfunctions of selfadjoint second order elliptic operators with low regularity assumptions on the coefficients. We prove that in two dimensions Courant's theorem holds also when the coefficients are just bounded and measurable. In the higher dimensional case, we prove a weakened version of Courant's theorem when the coefficients in the principal part are Hölder continuous.

About the article


Received: 1996-09-15

Published Online: 2008-03-11

Published in Print: 1998-09-01


Citation Information: Forum Mathematicum, Volume 10, Issue 5, Pages 521–532, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.10.5.521.

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